Etudes des proprietes des neutrinos dans les contextes ...

tel-00450051, version 1 - 25 Jan 2010
with x ≡ m2 τ /M2 W and αW ≡ α/s2 W . For a neutral unpolarized medium with
Ne = Np and arbitrary Nn one finds from Eq.(4.50) and Eq.(4.51):
m 2 τ
pν(nντ − nνµ) = GF 3α
√2
2π sin 2 θW m2 W
2 mτ × (Nn + Np) ln
Factorizing out (Nn + Np) and using the equality
one obtains:
pν(nντ − nνµ) = 3G2 F m2 τ
2π 2
= − √ 2GF
= − √ 2GF
GF =
απ
√ 2 sin 2 θWm 2 W
2 mτ ln
m2
+
W
Np
3 √ 2GFm 2 τ
(2π) 2 Ye
Y eff
τ
Ye
Ne
ln
m 2 τ
m 2 W
+
Nn + Np
2
3
2 mW + Yn
3
+ Np + 2
3
Nn
Nn + Np
− 1
Ne
(4.52)
(4.53)
(Nn + Np)
= − √ 2GFY eff
τ NB (4.54)
where NB is the baryon density in the medium. Thus, we can see these radiative
corrections as an effective matter of τ depending on the electron density Ne. For
an isoscalar medium with Nn = Np = Ne, we have:
and
pν(nντ − nνµ) = − √ 2GF
Y eff
τ
6 √ 2GFm 2 τ
(2π) 2
≃ 5.4 × 10−5
2 mW ln
m2
−
τ
5
Ne
6
Finally, the potential due to these one-loop radiative corrections is
Vµτ = √ 2GF
Vµτ = √ 2GF
3 √ 2GFm 2 τ
(2π) 2 Ye
ln
Y eff
τ
Ye
2 mW m 2 τ
(4.55)
(4.56)
Ne. (4.57)
+ Yn
3
− 1 Ne
(4.58)
Though this term seems very small, it is not negligible and can lead to effects
inside the supernova like a resonance between νµ and ντ neutrinos [61]. Contrary
to what was commonly thought, it can even leads to theoretically observable
effects on the νe and νe fluxes inside the supernova, affecting consequently Ye and
even on Earth, all of those via the presence of the CP-violating phase.
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